Propaganda authorities in China have failed to stem the torrent of public outrage over last Saturday's high-speed rail crash amid continuing aggressive media reporting and angry online posts.

Amid the rancour, China's premier, Wen Jiabao, ordered a "swift, open and transparent" investigation, adding that its results should be made public. He promised to take resolute steps to strengthen safety, the Xinhua state news agency reported.

At least 39 people died and more than 190 were injured in the crash near Wenzhou in Zhejiang province. Six carriages derailed and four plunged from a viaduct after one train smashed into the back of a stationary train.

Directives leaked this week ordered journalists to avoid analysing the causes and focus on uplifting stories of the rescue but several outlets continued to attack the handling of the collision and raise awkward questions – such as the whereabouts of the surviving train driver and whether the safety systems had failed.

It was also reported that the "miracle" rescue of a toddler happened only because the officer who found her defied orders to halt the search.

"Knowing how the railway's Great Leap was achieved, who can say that the high speed network is safe? ... unofficial opinions have been blocked and silence was imposed on dissenting experts. That is why tragedies are unavoidable," warned an editorial in the Economic Observer. Meanwhile, users posted millions of messages on Sina's Twitter-like Weibo service and some microbloggers referred to the railways ministry as "iron hooligans".

One created a fake movie poster, spoofing recent propaganda films. Titled The Panicked Train Crew, and featuring images of railway officials, it proclaims: "After the Founding of a Republic and The Beginning of the Great Revival, another epic film to celebrate the 90th anniversary of the Chinese Communist party!" Although critical reporting and online attacks on authorities are often seen after disasters, it is rare for them to continue for so long – particularly in the face of explicit orders. It is especially unusual given that high speed rail is regarded as a matter of national prestige.

New media professor Hu Yong said: "The difference this time is how widely it has spread, how sharp the criticism is and how much the various tiers of society are influenced."

He said microblogging had played a major role in spreading information and reaction, but added: "It is still questionable whether this will affect policy-making and the final outcome." David Bandurski, of the China Media Project at Hong Kong University, predicted that authorities would soon clamp down. He said the sensitivity of the political situation – with jockeying for position ahead of next year's power transition – had made the issue "too hot to handle".

Others have suggested that leaders may be keen to clip the wings of the overly powerful ministry. Bandurski also suggested journalists might be seeking to push back after a recent media clampdown: "When they do crack down on the story, everyone is going to know what they are not reading. The political blowback is going to be huge," he added.

Propaganda directives are issued by numerous bodies, which might help to explain variations in coverage, although at least one of the orders appeared to be at national level. Southern Metropolitan Daily warned: "Without independent investigation of the truth, the living will not agree and the dead will not rest." The Beijing Times said many "puzzles" remained unsolved.The state-run Global Times also attacked officials for failing to answer reasonable questions. "Chinese society is changing and public democracy is booming in the internet era, but the arrogance of certain authorities has stagnated ... public opinion in China cannot stand this anymore," said an editorial.

He Weifang, a prominent scholar at Peking University Law School, used his microblog account to call for an independent special commission to investigate the crash and the future development of high speed rail. He pointed out that the ministry of railways was affiliated to the state council, which has set up the current inquiry, adding: "If they investigate, it is hard to demonstrate justice and fairness."